{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import norm as gaussian\n",
    "from scipy.stats import multivariate_normal as gaussian_multi\n",
    "from scipy.stats import bernoulli as bern\n",
    "from scipy.stats import multinomial\n",
    "from scipy.stats import expon\n",
    "from scipy.stats import laplace\n",
    "from scipy.stats import binom\n",
    "from scipy.stats import poisson\n",
    "import numpy as np\n",
    "import matplotlib.pylab as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Normal Distribution\n",
    "x = np.linspace(-6,6,1000)\n",
    "mu, sigma = 0, 2\n",
    "plt.plot(x, gaussian.cdf(x,mu,sigma));\n",
    "plt.plot(x, gaussian.pdf(x,mu,sigma));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Multivariate Normal Distribution\n",
    "x = np.linspace(-6, 6, 1000)\n",
    "mu, sigma = 0,0.5 #Note: sigma in this case is the covariance matrix\n",
    "plt.plot(x, gaussian_multi.cdf(x,mu,sigma));\n",
    "plt.plot(x, gaussian_multi.pdf(x,mu,sigma));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Exponential Distribution\n",
    "x = np.linspace(expon.ppf(0.01), expon.ppf(0.99), 100)\n",
    "plt.plot(x, expon.pdf(x),'r-', lw=5, alpha=0.6, label='expon pdf');\n",
    "plt.plot(x, expon.cdf(x), 'b-', lw=5, alpha=0.5, label='expon cdf');\n",
    "plt.legend(loc='best', frameon=False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Laplace Distribution\n",
    "x = np.linspace(laplace.ppf(0.01),laplace.ppf(0.99), 100)\n",
    "plt.plot(x, laplace.pdf(x),'r-', lw=5, alpha=0.6, label='laplace pdf');\n",
    "plt.plot(x, laplace.cdf(x),'b-', lw=5, alpha=0.5, label='laplace cdf');\n",
    "plt.legend(loc='best', frameon=False) #Note: the purple is the overlap\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.04200000000000007"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Multinomial Distribution\n",
    "rv = multinomial(8, [0.3, 0.2, 0.5])\n",
    "rv.pmf([1, 3, 4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Bernoulli Distribution\n",
    "p = 0.3\n",
    "x = np.arange(bern.ppf(0.01, p),(bern.ppf(0.99,p))) # Note: ppf finds the value associated with the \n",
    "                                                    # given probability\n",
    "plt.plot(x, bern.pmf(x,p),'bo',ms=8,label='bernoulli pmf');\n",
    "plt.vlines(x,0,bern.pmf(x,p), colors='b', lw=5, alpha=0.5);\n",
    "#plot(x, bern.cdf(x,p));\n",
    "plt.legend(loc='best', frameon=False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Bionomial Distribution\n",
    "n, p = 5, 0.4\n",
    "x = np.arange(binom.ppf(0.01, n, p),binom.ppf(0.99, n, p))\n",
    "plt.plot(x, binom.pmf(x, n, p), 'bo', ms=8, label='binom pmf')\n",
    "plt.plot(x, binom.cdf(x, n, p), 'ro', ms=8, label='binom cdf')\n",
    "plt.vlines(x, 0, binom.pmf(x, n, p), colors='b', lw=5, alpha=0.5)\n",
    "plt.legend(loc='best', frameon=False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Poisson Distrubtion\n",
    "mu = 0.6\n",
    "x = np.arange(poisson.ppf(0.01, mu),poisson.ppf(0.99, mu))\n",
    "plt.plot(x, poisson.pmf(x, mu), 'bo', ms=8, label='poisson pmf')\n",
    "plt.plot(x, poisson.cdf(x, mu), 'ro', ms=8, label='poisson cdf')\n",
    "plt.vlines(x, 0, poisson.pmf(x, mu), colors='b', lw=5, alpha=0.5)\n",
    "plt.legend(loc='best', frameon=False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# More Distributions\n",
    "Can be found at (https://docs.scipy.org/doc/scipy/reference/stats.html)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
